Toeplitz operators with semi-almost-periodic matrix symbols on Hardy spaces

A. Böttcher; Yu I. Karlovich; I. Spitkovsky

doi:10.1023/A:1010683522795

Toeplitz operators with semi-almost-periodic matrix symbols on Hardy spaces

A. Böttcher, Yu I. Karlovich, I. Spitkovsky

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We establish a Fredholm criterion and an index formula for Toeplitz operators with semi-almost-periodic matrix symbols on the Hardy spaces H^p (1 < p < ∞). Our main result completes the Fredholm theory of the aforementioned operators and generalizes previous results, which concerned the case p = 2 or were based on certain additional assumptions, such as factorizability, for the almost-periodic representatives of the symbol.

Original language	English (US)
Pages (from-to)	115-136
Number of pages	22
Journal	Acta Applicandae Mathematicae
Volume	65
Issue number	1-3
DOIs	https://doi.org/10.1023/A:1010683522795
State	Published - Jan 2001

Keywords

Almost periodic function
Essential spectrum
Fredholm operator
Index formula
Spectrum
Toeplitz operator

ASJC Scopus subject areas

Applied Mathematics

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10.1023/A:1010683522795

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title = "Toeplitz operators with semi-almost-periodic matrix symbols on Hardy spaces",

abstract = "We establish a Fredholm criterion and an index formula for Toeplitz operators with semi-almost-periodic matrix symbols on the Hardy spaces Hp (1 < p < ∞). Our main result completes the Fredholm theory of the aforementioned operators and generalizes previous results, which concerned the case p = 2 or were based on certain additional assumptions, such as factorizability, for the almost-periodic representatives of the symbol.",

keywords = "Almost periodic function, Essential spectrum, Fredholm operator, Index formula, Spectrum, Toeplitz operator",

author = "A. B{\"o}ttcher and Karlovich, {Yu I.} and I. Spitkovsky",

note = "Funding Information: Yu.I.K. was partially supported by CONACYT (M{\'e}xico) grant, C{\'a}tedra Patrimonial, No. 99017-Ex and I.S. was partially supported by NSF Grant DMS-9988579.",

year = "2001",

month = jan,

doi = "10.1023/A:1010683522795",

language = "English (US)",

volume = "65",

pages = "115--136",

journal = "Acta Applicandae Mathematicae",

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TY - JOUR

T1 - Toeplitz operators with semi-almost-periodic matrix symbols on Hardy spaces

AU - Böttcher, A.

AU - Karlovich, Yu I.

AU - Spitkovsky, I.

N1 - Funding Information: Yu.I.K. was partially supported by CONACYT (México) grant, Cátedra Patrimonial, No. 99017-Ex and I.S. was partially supported by NSF Grant DMS-9988579.

PY - 2001/1

Y1 - 2001/1

N2 - We establish a Fredholm criterion and an index formula for Toeplitz operators with semi-almost-periodic matrix symbols on the Hardy spaces Hp (1 < p < ∞). Our main result completes the Fredholm theory of the aforementioned operators and generalizes previous results, which concerned the case p = 2 or were based on certain additional assumptions, such as factorizability, for the almost-periodic representatives of the symbol.

AB - We establish a Fredholm criterion and an index formula for Toeplitz operators with semi-almost-periodic matrix symbols on the Hardy spaces Hp (1 < p < ∞). Our main result completes the Fredholm theory of the aforementioned operators and generalizes previous results, which concerned the case p = 2 or were based on certain additional assumptions, such as factorizability, for the almost-periodic representatives of the symbol.

KW - Almost periodic function

KW - Essential spectrum

KW - Fredholm operator

KW - Index formula

KW - Spectrum

KW - Toeplitz operator

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DO - 10.1023/A:1010683522795

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SN - 0167-8019

VL - 65

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EP - 136

JO - Acta Applicandae Mathematicae

JF - Acta Applicandae Mathematicae

IS - 1-3

ER -

Toeplitz operators with semi-almost-periodic matrix symbols on Hardy spaces

Abstract

Keywords

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